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Exercise

dydx(ln y cos x = x3+2xy +1)\frac{dy}{dx}\left(ln\:y\:cos\:x\:=\:x^3+2xy\:+1\right)

Step-by-step Solution

1

Applying the product rule for logarithms: log⁡b(MN)=log⁡b(M)+log⁡b(N)\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)

dydxln⁡(y)+ln⁡(cos⁡(x))=x3+2xy+1\frac{dy}{dx}\ln\left(y\right)+\ln\left(\cos\left(x\right)\right)=x^3+2xy+1

Final answer to the exercise

dydxln⁡(y)+ln⁡(cos⁡(x))=x3+2xy+1\frac{dy}{dx}\ln\left(y\right)+\ln\left(\cos\left(x\right)\right)=x^3+2xy+1

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Similar Questions Solved

derivdef(ln⁡(x))derivdef\left(\ln\left(x\right)\right)

Main Topic: Properties of Logarithms

They are properties that can help us simplify expressions with logarithms.

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dydx (ln y cos x = x3+2xy +1)
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